How many meters to the moon. The distance from our Earth to the only satellite of the planet - the Moon. Distance to the moon
In an elliptical orbit, which means that at some point it will be farther, and at some, on the contrary, closer.
That is why 384,403 km is considered the average distance to the Moon or, as astronomers say, is the "semi-major axis of the Moon's orbit." When the Moon is at the point closest to the Earth (perigee), we are only 363,104 km apart. And the distance from the most distant point (apogee) to the Earth is as much as 406 696 km.
It turns out that the distance from the Earth to the Moon varies within 43,592 km. It is thanks to this rather big difference The moon in the night sky comes in different sizes. At perigee, the Moon looks to us 15% larger than at its apogee.
The difference in distance also affects the brightness of the moon when it reaches its full phase. At the point closest to Earth, the full moon is usually 30% brighter than at its maximum distance from our planet. When the full moon is at perigee, it is called the "supermoon".
In the video ("One Year of the Moon in 2.5 Minutes"), you can admire the Moon in all its changing beauty:
A very logical question arises: how do we know at what distance the moon is? The answer depends on which era we are talking about. IN Ancient Greece for example, astronomers used their knowledge of geometry for their calculations.
For a long time, the ancient Greeks observed shadows and found that when an object is in front, its shadow is 108 times its actual diameter. So a ball with a diameter of 2.5 cm, placed on a stick between the Sun and the surface of the Earth, will give a triangular shadow 270 cm long.
This observation was later used to study lunar and solar eclipses. During a lunar eclipse, the Greeks noticed that the satellite was not completely covered by the shadow of the Earth, and the width of this shadow was about 2.5 times the Moon. During a solar eclipse, it was noted that the size of the moon and its location at that moment were sufficient to completely block the sun. The shadow she cast ended on Earth, and at the same angle as the shadow from the Earth, which made both shadows two versions of the same triangle, only of different sizes.
The Greeks concluded that the base of the larger of the two triangles would be equal to one diameter of the Earth (at that time this figure had already been calculated and amounted to 12,875 km), and its length - 1,390,000 km. The smaller triangle will be 2.5 times wider than the diameter of the Moon, and since the triangles are proportional, its height will be 2.5 times the height of the moon's orbit. By connecting these triangles, the Greeks obtained the equivalent of 3.5 lunar orbits. By dividing the previously calculated value of 1.39 million km by 3.5, they obtained a relatively accurate distance to the Moon, equal to 397,500 km. Not bad at all for an ancient people!
Now the distance to the moon can be calculated to within a few millimeters. It is enough for scientists to detect how long it takes for a laser beam, launched from Earth, to reach a special reflector installed on the Moon and return back.
Determination of the so-called laser ranging of the Moon became possible more than forty years ago, after the astronauts of the Apollo mission installed a series of reflectors on the surface of our satellite. A laser beam shot from Earth is reflected from one of these reflectors and returns to our planet.
True, out of 100 quadrillion photons shot towards the Moon, not so many return to the Earth, but this is enough for a highly accurate calculation of the distance.
Because the speed of light is nearly 300,000 km / s, and the laser beam takes just over a second to reach the lunar surface. The return journey takes the same amount of time. By fixing the exact time it took light to get to the moon and back, astronomers then easily calculate the exact distance to the moon in this moment time.
Thanks to this method of calculating the distance, scientists have learned that the moon is slowly moving away from our planet. Every year - by 3.8 cm. This means that in millions of years the Moon in the sky will seem smaller than it appears to us now. And in a billion years or so, the Moon will look smaller than the Sun, and total solar eclipses will forever be a thing of the past.
The ancient Greeks tried to measure the distance from the Earth to the Moon.
Only the composition has come down to us Aristarchus of Samos"On the magnitudes and distances of the Sun and the Moon" (III century BC), where he, for the first time in the history of science, tried to establish the distances to these celestial bodies and their sizes.
Aristarchus approached the solution of this issue very wittily. He proceeded from the assumption that the Moon has the shape of a ball and shines with light reflected from the Sun. In this case, at those moments when the Moon has the form of a half-disk, it forms right triangle with the Earth and the Sun:
If at this moment you can accurately determine the angle between the directions from the Earth to the Moon and the Sun (CAB), you can find from simple geometric relationships how many times the leg (distance from the Earth to the Moon AB) is less than the hypotenuse (the distance from the Earth to the Sun AC). According to Aristarchus, CAB = 87 °; therefore, the ratio of these sides is 1:19.
Aristarchus was mistaken about 20 times: in reality, the distance to the Moon is less than to the Sun, almost 400 times. The catch is that it is impossible to accurately determine the moment when the moon is at the apex of a right angle, only on the basis of observations. The slightest inaccuracy entails a huge deviation from the true value.
The greatest astronomer of antiquity, Hipparchus of Nicea in the middle of the 2nd century BC. e. determined with great confidence the distance to the moon and its dimensions, taking the radius of the globe as a unit.
In his calculations, Hipparchus proceeded from the correct understanding of the cause of lunar eclipses: the moon falls into the earth's shadow, which has the shape of a cone with a top located somewhere in the direction of the moon.
Diagram explaining the definition of the radius of the moon by the method of Aristarchus.
Byzantine copy of the 10th century.
Take a look at the picture. It shows the position of the Sun, Earth and Moon during a lunar eclipse. It follows from the similarity of triangles that the distance from the Earth to the Sun AB is as many times greater than the distance from the Earth to the Moon BC, how many times the difference between the radii of the Sun and the Earth (AE - BF) is greater than the difference between the radii of the Earth and its shadow at the distance of the Moon (BF - CG ).
From observations using the simplest goniometric instruments, it followed that the radius of the moon is 15 ", and the radius of the shadow is approximately 40", that is, the radius of the shadow is almost 2.7 times the radius of the moon. Taking the distance from the Earth to the Sun as a unit, it was possible to establish that the radius of the Moon is almost 3.5 times less than the radius of the Earth.
It was already known that an object is observed at an angle of 1 ", the distance to which exceeds its dimensions by 3,483 times. Consequently, Hipparchus reasoned, at an angle of 15" the observed object will be 15 times closer. This means that the Moon is at a distance of 230 times (3 483: 15) greater than its radius. And if the radius of the Earth is approximately 3.5 times the radius of the Moon, then the distance to the Moon is 230: 3.5 ~ 60 times the radius of the Earth, or about 30 Earth's diameters (this is about 382 thousand kilometers).
In our time, the measurement of the distance from the earth to the moon was carried out using the method of laser ranging. The essence of this method is as follows. A corner reflector is installed on the surface of the moon. From the ground, a laser beam is directed to the reflector mirror with the help of a laser. At the same time, the time when the signal was emitted is precisely recorded. The light reflected from the device on the Moon returns to the telescope within about one second. Having determined the exact time during which a ray of light travels the distance from the Earth to the Moon and back, you can set the distance from the radiation source to the reflector.
Using this method, the distance from the earth to the moon is determined with an accuracy of several kilometers (the maximum measurement accuracy is currently 2-3 centimeters!): On average, it is 384 403 km... "On average" not because this distance is taken from different or approximate measurements, but because the Moon's orbit is not a circle, but an ellipse. At the apogee (the point of the orbit farthest from the Earth), the distance from the center of the Earth to the Moon is 406 670 km, at perigee (the closest point of the orbit) - 356 400 km.
It is no secret that people have long dreamed of flying into space - the unexplored vast expanses fascinate and beckon, but space tourism has not yet become a mass industry. Why is that? Because getting to another planet is not so easy. Even the Moon, which seems to be a stone's throw when we look at it at night, is many kilometers. How long does it take to reach the moon?
Distance from Earth to Moon
The average distance from the Earth to the Moon is 384 399 km.
We say average, because the Moon's orbit is not circular, but elliptical, which means that the distance between the Earth and the Moon is changing. At perigee - the closest point to the Earth - the distance is 363 104 km, at the apogee - the most distant point - 405 696 km.
So, we know the distance, which means that in order to find the time it takes to get to the moon, you just need to divide it by the speed. Based on this fact, we get:
- Walk to the moon for 9 years (and you will have to walk continuously at a speed of 5 km / h).
- By car (if you take an average speed of 100 km / h and, again, do not make stops), you can get to the Moon in 160 days.
- The plane (average speed 800 km / h) will fly in 20 days.
- A modern Apollo-class spacecraft will be able to reach the Moon in three days.
As you can see, the path is not short, and not everyone is able to withstand so much time of continuous flight, while it is worth considering that the flight would cost a fabulous amount of money.
Measurement of the distance from the Earth to the Moon was carried out in ancient times: the Greeks tried to do this repeatedly.
This information was necessary for a person to get a complete picture of the concept of the Universe.
In addition to calculating the distance to the Earth's satellite, the ancient Greeks carried out calculations to calculate its radius.
Over time, technological progress has developed and today all measurements are known to man.
For a long time, people were interested in what space and the moon are - since time immemorial it has been a natural satellite of our planet.
People were interested in how far it was and how long to fly to it, using various calculations for this.
To date, measure the distance by the methods used in Everyday life- unrealistic.
For this, trigonometric formulas and calculations are used.
Consider how the ancient people defined this indicator, recalling that it is measured from the center of the satellite:
- The first who tried to get through to the truth was Aristarchus of Samos.
On the basis of geometric equations and indicators obtained using goniometric instruments, the scientist conducted a study.
To begin with, he calculated the difference in the distance to the satellite and the Sun, after which he multiplied given result to the radius of the Earth. His calculations showed that the distance is 509680 in kilometers.
- In the 2nd century BC, the astronomer Hipparchus of Nicaea also set about calculating.
He conducted observations of the Moon at different phases and came to the conclusion that the distance to the Earth would be equal to 382260 kilometers.
Based on angular measurements, Hipparchus found out that during the eclipse, the Sun and the Moon have the same indicators.
After that, he calculated the difference and derived a formula by which he determined the average distance.
Average distance in kilometers
It is impossible to indicate the exact indicators of the distance in kilometers: this is due to the elliptical shape of the orbit along which the satellite moves.
This suggests that for some time it moves away from the planet, after which it approaches again.
Note! There are several numerical results that describe the mileage of the distance to a celestial satellite.
The actual dimensions can vary within 15%, which is associated with different points of the satellite.
The fullest Moon is much closer to the Earth than when it goes through the growth phase.
Known indicators will help to find out the distance that scientists have measured:
Flight time
To date, a large number of flights have already been completed in order to judge how long it takes to travel to the satellite.
Scientists made calculations based on rocket speed and astronaut observations.
Here are some numbers:
- The slowest flight will take 1 year 1 month and 2 weeks, which has been proven experimentally.
In 2003, a lunar probe was launched on the basis of a revolutionary ion engine station called ESA SMART-1.
- The average flight took 5 days when the Chinese satellite Chang'e-1 was sent into orbit in 2007, using standard rocket engines.
- The manned flight with a man lasted 3 days, 3 hours and 49 minutes, when the Americans first stepped onto the lunar surface in 1969 - the Saturn 5 spacecraft took off from a platform in Florida.
- The shortest route was mastered by the Americans in the New Horizons project: the satellite's speed is 58 thousand kilometers.
To overcome the pull of the sun, Nasa used tremendous acceleration.
Important! The Soviet satellite Luna-1 made its first flight, it passed 500 kilometers from the Moon, reaching the place in 2 days.
Today, space travel companies around the world offer short or long duration trips to the moon.
Any calculations made by a person were surrounded by many interesting facts, stories. Measurement of space and distance to the Moon is not devoid of such cases.
Here are some interesting examples related to the history of calculating the flight time, the distance from the Earth to the satellite:
- According to legend, the Moon was formed from the collision of the planet Earth with another planet. Then an orbit was formed, from which a yellow-white satellite was formed.
- The satellite is always facing the planet with one side.
- The largest crater is called Bailey, with a diameter of 295 kilometers.
- During one of the expeditions, the American Apollo 6 brought several hundred kilograms of lunar soil to Earth.
- Being on Earth and looking at the sky, it seems that the Moon and the Sun have the same size.
- There is no atmosphere on the moon, so night falls there immediately, without the gradual extinction of light.
- The force of gravity on the satellite has smallest value- it is 6 times less than the force of gravity on Earth.
- On the surface of the satellite there is a monument to the fallen cosmonauts - this is a 10 centimeters figure made of aluminum.
- Over the years, the Moon has significantly moved away from the Earth: this happens every year by 4 centimeters.
- The minimum distance at the nearest points from the Moon to Mars is 55 million 399 thousand kilometers.
It is known that regular flights to Mars are planned in the future, but it is much more convenient to carry them out from the surface of the satellite.
Calculating the distances to the moon helps flight planners to reliably calculate the amount of fuel, as well as the money spent on the flight.
Useful video
One of the main character traits of any person is curiosity. It is to her that humanity owes the majority scientific discoveries and the benefits of technological progress based on them. Since ancient times, people have gazed with interest at the night sky, in which countless stars were shining, and the moon was slowly floating across the sky. It is not surprising that since then the dream of visiting some heavenly body has not left a person.
The invention of the telescope confirmed the assumption that the Moon is at the minimum distance from the Earth. From that moment on, science fiction writers in their novels sent fearless travelers to this heavenly body. It is interesting that the proposed methods were fully consistent with the spirit of their time: a projectile, a rocket based on a jet engine, an antigravitational substance Keyword (H. Wells), etc. True, no one could say exactly how long to fly to the Moon.
Quite a long time has passed since then. Although the term "a lot" is applicable to the duration of human life, but for history, only a moment has passed. Now the natural is increasingly viewed not just as an abstract goal of flight, but as the basis for the bases of the future. These include settlements under a heavy-duty dome, sealed cities below the surface, automatic observatories, and gas stations for spaceships... Truly, the flight of fantasy has no boundaries. Surprisingly, at the same time, many do not even know how much to the moon.
Now the distance from the Earth to the satellite is calculated with high accuracy. Therefore, knowing the speed, you can calculate how long it takes to fly to the moon. It is known that the distance between the central points of these celestial bodies is 384 400 km. But since you need to know the path between the surfaces to determine the travel time, you need to subtract the values of the radii. It is 6378 km for the Earth, and 1738 km for the satellite. The exact answer to the question: "How long to fly to the moon?" suggests the need to take into account the features of the orbit of our natural satellite... As you know, the Moon is close to an oval (that is, elliptical), so the path length varies by as much as 12%, which is quite a lot. So, at the closest approach (perigee), the distance is 363 104 km, but at the far point (apogee) it is already 405 696 km. Taking into account the sum of their radii, we subtract the known values from the smaller number and as a result we get 354 988 km. This is the distance from the Earth to the lunar surface.
Based on the distance voiced above, you can definitely say how long to fly to the moon. It remains only to take into account the speed with which it is planned to carry out such a desired journey. So, the flight time to the surface of a natural satellite depends on the chosen vehicle and takes:
160 days when driving a car traveling at a speed of about 100 km / h;
Accordingly, an airplane flying at least 800 km per hour will take “only” 20 days;
The ships of the American Apollo program reached the surface of our satellite in three days and four hours;
Having developed the second at 11.2 km / s, it will be possible to cover the distance in 9.6 hours;
Having turned into pure energy (remember Arthur Clarke's "Space Odyssey") and moving from (300,000 km / s), the goal can be achieved in a paltry 1.25 s;
Well, for the adherents of the saying: "The quieter you go - the further you will be!" you will have to spend at least nine years if you continuously walk at a regular pace at a speed of 5 km / h.
Obviously, the question is: "How long to fly to the moon?" at the present time it can already be considered resolved. It remains only to choose a vehicle, then, depending on the decision made, stock up on the proper patience, the required amount of provisions and hit the road.
